EMS Staffing and Support Act This bill provides funding for FY2023 and each fiscal year thereafter to support organizations that provide medical transport and emergency medical services (i.e., EMS organizations). It also requires the Department of Health and Human Services to report on reimbursement and other challenges faced by EMS organizations, including in rural areas. Specifically, the Health Resources and Services Administration (HRSA) must establish a competitive grant program for state, territorial, tribal, and local governments; nonprofit EMS organizations; and nonprofits that represent the interests of EMS organizations. Grant funds may be used for training and other personnel costs, purchasing necessary equipment and supplies, and related purposes. The bill further requires HRSA to allocate funding through compacts or contracts to Indian tribes for such purposes.